On distance integral and distance Laplacian integral graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908871665123328 |
|---|---|
| author | Pirzada, S. Mushtaq, Ummer de Lima, Leonardo |
| author_facet | Pirzada, S. Mushtaq, Ummer de Lima, Leonardo |
| contents | Let $G$ be a connected graph on $n$ vertices and let $D(G)$ and $D^{L}(G)$ be the distance and the distance Laplacian matrices associated with $G$. A graph $G$ is said to be $D$-integral (resp. $D^L$-integral) if all eigenvalues of $D(G)$ (resp. $D^L(G)$) are integers. In this paper, we obtain various conditions under which the graphs $a\overline{K_m}\nabla C_n$ and $K_{p,p}\nabla C_n$ are distance integral. We also obtain conditions on $m$, $n$ under which the dumbbell graph $\boldsymbol{DB}(W_{m,n})$ is $D^L$-integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07232 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On distance integral and distance Laplacian integral graphs Pirzada, S. Mushtaq, Ummer de Lima, Leonardo Combinatorics Spectral Theory 05C50 Let $G$ be a connected graph on $n$ vertices and let $D(G)$ and $D^{L}(G)$ be the distance and the distance Laplacian matrices associated with $G$. A graph $G$ is said to be $D$-integral (resp. $D^L$-integral) if all eigenvalues of $D(G)$ (resp. $D^L(G)$) are integers. In this paper, we obtain various conditions under which the graphs $a\overline{K_m}\nabla C_n$ and $K_{p,p}\nabla C_n$ are distance integral. We also obtain conditions on $m$, $n$ under which the dumbbell graph $\boldsymbol{DB}(W_{m,n})$ is $D^L$-integral. |
| title | On distance integral and distance Laplacian integral graphs |
| topic | Combinatorics Spectral Theory 05C50 |
| url | https://arxiv.org/abs/2603.07232 |